Electronic Communications in Probability

Concentration inequalities via Malliavin calculus with applications

John Treilhard and Abdol-Reza Mansouri

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Abstract

We use the Malliavin calculus to prove a new abstract concentration inequality result for zero mean, Malliavin differentiable random variables which admit densities. We demonstrate the applicability of the result by deriving two new concrete concentration inequalities, one relating to an integral functional of a fractional Brownian motion process, and the other relating to the centered maximum of a finite sum of Normal random variables. These concentration inequalities are, to the best of our knowledge, largely unattainable via existing methods other than those which are the subject of this paper.

Article information

Source
Electron. Commun. Probab., Volume 20 (2015), paper no. 36, 14 pp.

Dates
Accepted: 8 May 2015
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465320963

Digital Object Identifier
doi:10.1214/ECP.v20-3931

Mathematical Reviews number (MathSciNet)
MR3352331

Zentralblatt MATH identifier
06473035

Subjects
Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus
Secondary: 60G22: Fractional processes, including fractional Brownian motion

Keywords
Malliavin calculus concentration inequalities fractional Brownian motion

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Treilhard, John; Mansouri, Abdol-Reza. Concentration inequalities via Malliavin calculus with applications. Electron. Commun. Probab. 20 (2015), paper no. 36, 14 pp. doi:10.1214/ECP.v20-3931. https://projecteuclid.org/euclid.ecp/1465320963


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